Econometrics

Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". The first known use of the term "econometrics" (in cognate form) was by Polish economist Paweł Ciompa in 1910. Jan Tinbergen is considered by many to be one of the founding fathers of econometrics. Ragnar Frisch is credited with coining the term in the sense in which it is used today.Read all..

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Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships.[1] More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference".[2] An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships".[3] The first known use of the term "econometrics" (in cognate form) was by Polish economist Paweł Ciompa in 1910.[4]Jan Tinbergen is considered by many to be one of the founding fathers of econometrics.[5][6][7]Ragnar Frisch is credited with coining the term in the sense in which it is used today.[8]

Basic models: linear regression

A basic tool for econometrics is the multiple linear regression model.[9] In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently used starting point for an analysis.[9] Estimating a linear regression on two variables can be visualised as fitting a line through data points representing paired values of the independent and dependent variables.

Okun's law representing the relationship between GDP growth and the unemployment rate. The fitted line is found using regression analysis.

For example, consider Okun's law, which relates GDP growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate (ΔUnemployment{\displaystyle \Delta \ {\text{Unemployment}}}) is a function of an intercept (β0{\displaystyle \beta _{0}}), a given value of GDP growth multiplied by a slope coefficient β1{\displaystyle \beta _{1}} and an error term, ε{\displaystyle \varepsilon }:

The unknown parameters β0{\displaystyle \beta _{0}} and β1{\displaystyle \beta _{1}} can be estimated. Here β1{\displaystyle \beta _{1}} is estimated to be −1.77 and β0{\displaystyle \beta _{0}} is estimated to be 0.83. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 1.77 points. The model could then be tested for statistical significance as to whether an increase in growth is associated with a decrease in the unemployment, as hypothesized. If the estimate of β1{\displaystyle \beta _{1}} were not significantly different from 0, the test would fail to find evidence that changes in the growth rate and unemployment rate were related. The variance in a prediction of the dependent variable (unemployment) as a function of the independent variable (GDP growth) is given in polynomial least squares.

One of the fundamental statistical methods used by econometricians is regression analysis.[15] Regression methods are important in econometrics because economists typically cannot use controlled experiments. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. Observational data may be subject to omitted-variable bias and a list of other problems that must be addressed using causal analysis of simultaneous-equation models.[16]

In addition to natural experiments, quasi-experimental methods have been used increasingly commonly by econometricians since the 1980s, in order to credibly identify causal effects.[17]

Example

A simple example of a relationship in econometrics from the field of labour economics is:

This example assumes that the natural logarithm of a person's wage is a linear function of the number of years of education that person has acquired. The parameter β1{\displaystyle \beta _{1}} measures the increase in the natural log of the wage attributable to one more year of education. The term ε{\displaystyle \varepsilon } is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, β0 and β1{\displaystyle \beta _{0}{\mbox{ and }}\beta _{1}} under specific assumptions about the random variable ε{\displaystyle \varepsilon }. For example, if ε{\displaystyle \varepsilon } is uncorrelated with years of education, then the equation can be estimated with ordinary least squares.

If the researcher could randomly assign people to different levels of education, the data set thus generated would allow estimation of the effect of changes in years of education on wages. In reality, those experiments cannot be conducted. Instead, the econometrician observes the years of education of and the wages paid to people who differ along many dimensions. Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education. For example, people born in certain places may have higher wages and higher levels of education. Unless the econometrician controls for place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages.

The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above. Exclusion of birthplace, together with the assumption that ϵ{\displaystyle \epsilon } is uncorrelated with education produces a misspecified model. Another technique is to include in the equation additional set of measured covariates which are not instrumental variables, yet render β1{\displaystyle \beta _{1}} identifiable.[18] An overview of econometric methods used to study this problem were provided by Card (1999).[19]

Limitations and criticisms

Like other forms of statistical analysis, badly specified econometric models may show a spurious relationship where two variables are correlated but causally unrelated. In a study of the use of econometrics in major economics journals, McCloskey concluded that some economists report p-values (following the Fisherian tradition of tests of significance of point null-hypotheses) and neglect concerns of type II errors; some economists fail to report estimates of the size of effects (apart from statistical significance) and to discuss their economic importance. She also argues that some economists also fail to use economic reasoning for model selection, especially for deciding which variables to include in a regression.[21][22]

In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects.[23] In such cases, economists rely on observational studies, often using data sets with many strongly associated covariates, resulting in enormous numbers of models with similar explanatory ability but different covariates and regression estimates. Regarding the plurality of models compatible with observational data-sets, Edward Leamer urged that "professionals ... properly withhold belief until an inference can be shown to be adequately insensitive to the choice of assumptions".[23]

1 2 3 Greene, William (2012). "Chapter 1: Econometrics". Econometric Analysis (7th ed.). Pearson Education. pp.47–48. ISBN9780273753568. Ultimately, all of these will require a common set of tools, including, for example, the multiple regression model, the use of moment conditions for estimation, instrumental variables (IV) and maximum likelihood estimation. With that in mind, the organization of this book is as follows: The first half of the text develops fundamental results that are common to all the applications. The concept of multiple regression and the linear regression model in particular constitutes the underlying platform of most modeling, even if the linear model itself is not ultimately used as the empirical specification.